Deformation/rigidity theoryと冨田・竹崎理論
变形/刚性理论和富田竹崎理论
基本信息
- 批准号:20K14324
- 负责人:
- 金额:$ 2.66万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Early-Career Scientists
- 财政年份:2020
- 资助国家:日本
- 起止时间:2020-04-01 至 2024-03-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
フォンノイマン環とは,(簡単に言えば)無限次元の行列環の事である.特にトレース写像を持たない場合に,III型フォンノイマン環という.これは物理学にも現れる自然な研究対象であり,私はこれを数学的な視点から研究している.本研究は,トレース写像を持つ場合に得られた近年の研究結果を,III型の場合に再現する事を基本的目標としている. 特に冨田竹崎理論の重要な道具である連続核を用いた研究を行う.今年度も,前年度に引き続きHaagerup-Stormer予想(1991)に取り組んだ.これはIII型フォンノイマン環の自己同型に関する予想であり,非常にいい加減に説明すると以下のようなものである:環上の状態(良い線形汎関数の事)の性質をあまり変えない自己同型はモジュラー作用素しかない.従順環(物理学に現れるクラス)については成り立つ事が知られており,非従順環の場合に成り立つ例は,私とC. Houdayer氏の共同研究によって前年度に得られていた.ただし前年度に得られた例は全て,almost periodicと呼ばれるクラスに入っていた.今年度はこのalmost periodicという仮定をはずした例を探した.結果として,前年度の研究で得た主定理の一つを一般化する事に成功した.これを用いてalmost periodicでない場合の例が得られるはずであるが,これはまだ現在も研究中である.これらの証明では上述した近年の研究結果の一つである「二つの状態に対するintertwiningの技術」が本質的な役割を果たしている.
This study focuses on the study of the nature of the environment, the study of physics, the study of the nature of nature, the study of mathematics, the study of mathematics, and the study of mathematics. According to the research results of recent years, the basic purpose of the study was rediscovered. Takesaki Takesaki Theory of Takesaki, Takesaki, Takeshi, Takesaki, Takasaki, Takesaki, Tak In the previous year, I would like to (1991) collect the information of the organization. The environment of the same type of Haagerup-Stormer would like to have the same kind of information. It is very important to know that the following information is required: the following information: the following is the most important thing: the following is the best way to know that you are the same type of person. Private C. Houdayer's joint study of the previous year received a full list of cases in the previous year, and almost periodic called for a review of the previous year. This year, we have received a review of the general situation in the previous year. This year, we have made a survey of the general situation in the previous year. The previous year's study concluded that the results of the previous year's study concluded that the results of the previous year's study were successful. The results of the previous year's study showed that the results of the previous year's study showed that the results of the previous year's study concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been successful. The results of the previous year's study had been concluded that the results of the previous year's study had been concluded that the results of the previous year's study had been successful.
项目成果
期刊论文数量(13)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras
阶乘、Connes III 型不变量和合并自由积冯诺依曼代数的完备性
- DOI:10.1017/prm.2018.152
- 发表时间:2020
- 期刊:
- 影响因子:0
- 作者:Cyril Houdayer;Yusuke Isono
- 通讯作者:Yusuke Isono
Note on bi-exactness for creation operators on Fock spaces
关于 Fock 空间上创建算子的双精确性的注释
- DOI:10.2969/jmsj/86338633
- 发表时间:2022
- 期刊:
- 影响因子:0.7
- 作者:HASEGAWA Kei;ISONO Yusuke;KANDA Tomohiro
- 通讯作者:KANDA Tomohiro
Ergodic theory of affine isometric actions on Hilbert spaces
希尔伯特空间上仿射等距作用的遍历理论
- DOI:10.1007/s00039-021-00584-2
- 发表时间:2021
- 期刊:
- 影响因子:2.2
- 作者:Yuki Arano;Yusuke Isono;Amine Marrakchi
- 通讯作者:Amine Marrakchi
Boundary and Rigidity of Nonsingular Bernoulli Actions
非奇异伯努利作用的边界和刚性
- DOI:10.1007/s00220-021-04134-7
- 发表时间:2022
- 期刊:
- 影响因子:2.4
- 作者:Hasegawa Kei;Isono Yusuke;Kanda Tomohiro
- 通讯作者:Kanda Tomohiro
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磯野 優介其他文献
磯野 優介的其他文献
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{{ truncateString('磯野 優介', 18)}}的其他基金
作用素環を用いた群作用の研究
使用算子代数研究群行为
- 批准号:
24K06759 - 财政年份:2024
- 资助金额:
$ 2.66万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Rigidity theoryの技術を用いたIII型フォンノイマン環の研究
利用刚性理论技术研究III型冯诺依曼环
- 批准号:
15J01338 - 财政年份:2015
- 资助金额:
$ 2.66万 - 项目类别:
Grant-in-Aid for JSPS Fellows
相似海外基金
冨田-竹崎理論の非有界作用素環への拡張とその量子物理への応用
富田-竹崎理论对无界算子代数的推广及其在量子物理中的应用
- 批准号:
08640246 - 财政年份:1996
- 资助金额:
$ 2.66万 - 项目类别:
Grant-in-Aid for Scientific Research (C)